JEE Main & Advanced JEE Main Paper (Held on 12-4-2019 Morning)

  • question_answer
    Which of the following combinations has the dimension of electrical resistance (\[{{\varepsilon }_{0}}\]is the permittivity of vacuum and \[{{\mu }_{0}}\]is the permeability of vacuum)?          [JEE Main Held on 12-4-2019 Morning]

    A) \[\sqrt{\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}}\]                                

    B) \[\frac{{{\mu }_{0}}}{{{\varepsilon }_{0}}}\]

    C) \[\sqrt{\frac{{{\mu }_{0}}}{{{\varepsilon }_{0}}}}\]        

    D) \[\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}\]

    Correct Answer: C

    Solution :

    \[[{{\varepsilon }_{0}}]={{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}\]              \[[{{\mu }_{0}}]=ML\,{{T}^{-2}}{{A}^{-2}}\]       \[[R]=M{{L}^{2}}\,{{T}^{-3}}{{A}^{-2}}\]          \[[R]=\left[ \sqrt{\frac{{{\mu }_{0}}}{{{\varepsilon }_{0}}}} \right]\]                 


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